Problem 1 (60 points) This problem is in two parts. wwwroo Vin (t) R ii. L C a) (20 points) The above circuit has R = 1kn, C = 0.25μF and

L = 1H. If the input to the circuit is vin (t) = 10 cos(wt +30°) V, with w = 377 rad/sec, find the output response by first (10 points) finding the circuit's transfer function magnitude and phase, for the given value of w, then (10 points) finding the steady state output as a time function, based on your magnitude and phase computation. T(s) = b) (40 points) Let's use the same above circuit, except that we now set L = 62.5 mH, and the input is now an arbitrary unspecified sinusoid. Follow these two sub-parts: i. (10 points) Show that the transfer function in this case becomes: + Vout (t) 8000² (s +8000)² (30 points) Print the blank semi-log graph template given on the next page. Then, use it to draw the Bode plot (using the straight-line approximations) for the gain of the above transfer function, using a dB scale for the gain on the y-axis and frequency (w) on a log-scale on the x-axis. You must complete the Bode plot by hand, and not using a computer-generated plot. Mark all passband gains, corner frequencies, or stopband slopes. Hint: factor the transfer function into the product of two identical transfer functions.